Classify polygons based on their sides and angles.

Objectives

6.1: Properties of Polygons

Vocabulary SketchThings to

Remember

PolygonA closed figure formed by 3 or more segments that intersect

only at their endpoints.

DiagonalA segment that connects

non-consecutive vertices.

Quadrilateral

A four-sided polygon.

Pentagon A five-sided polygon.

Hexagon A six-sided polygon.

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6

5

Vocabulary SketchThings to

Remember

Heptagon A seven-sided polygon.

Octagon An eight-sided polygon.

Nonagon A nine-sided polygon.

Decagon A ten-sided polygon.

Dodecagon

A twelve-sided polygon.

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8

10

12

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Vocabulary Sketch Things to Remember

n-gon A polygon with n number of sides.

Regular Polygon

An equilateral AND equiangular polygon.

Irregular Polygon

Any polygon that is NOT regular.

Concave Polygon

Any part of the diagonal lies in the exterior of the

polygon.

Convex Polygon

All diagonals lie in the interior of the polygon.

Each segment that forms a polygon is a side of the polygon. The common endpoint of two sides is a vertex of the polygon. A segment that connects any two nonconsecutive vertices is a diagonal.

6.1: Properties of Polygons

Tell whether the figure is a polygon. If it is a polygon, name it by the number of sides.

polygon, hexagon

1.

Example 1B: Identifying Polygons

Tell whether the figure is a polygon. If it is a polygon, name it by the number of sides.

polygon, heptagon

2.

Example 1C: Identifying Polygons

Tell whether the figure is a polygon. If it is a polygon, name it by the number of sides.

not a polygon

3.

Check It Out! Example 1a

Tell whether each figure is a polygon. If it is a polygon, name it by the number of its sides.

not a polygon

4.

Check It Out! Example 1b

Tell whether the figure is a polygon. If it is a polygon, name it by the number of its sides.

polygon, nonagon

5.

Check It Out! Example 1c

Tell whether the figure is a polygon. If it is a polygon, name it by the number of its sides.

not a polygon

6.

All the sides are congruent in an equilateral polygon. All the angles are congruent in an equiangular polygon. A regular polygon is one that is both equilateral and equiangular. If a polygon is not regular, it is called irregular.

A polygon is concave if any part of a diagonal contains points in the exterior of the polygon. If no diagonal contains points in the exterior, then the polygon is convex. A regular polygon is always convex.

Tell whether the polygon is regular or irregular. Tell whether it is concave or convex.

irregular, convex

7.

Tell whether the polygon is regular or irregular. Tell whether it is concave or convex.

irregular, concave

8.

Tell whether the polygon is regular or irregular. Tell whether it is concave or convex.

regular, convex

9.

Tell whether the polygon is regular or irregular. Tell whether it is concave or convex.

regular, convex

10.

Tell whether the polygon is regular or irregular. Tell whether it is concave or convex.

irregular, concave

11.